Unit 7: Hypothesis Testing — Short Questions

A hypothesis is an assumption or statement made in research before testing begins, which can be tested using data. It predicts an outcome and must be clear and measurable so that it can guide and focus the study.

A research question defines what is being studied. It guides data collection, and a hypothesis is formed from it as a possible answer. Clear research questions lead to clear, focused hypotheses.

The null hypothesis (H0) is the default assumption that there is no significant effect, difference, or relationship between variables. Data is tested against this hypothesis, and it is rejected only if evidence against it is strong.

A test statistic is a numerical value calculated from sample data that is used to make a decision in hypothesis testing. It summarizes how far the sample results are from what is expected under the null hypothesis. Examples include the z-value, t-value, and F-value.

The p-value is the probability of obtaining the observed result, or a more extreme one, if the null hypothesis is true. A small p-value (e.g., less than α = 0.05) provides strong evidence against the null hypothesis and supports its rejection.

The critical region is the area of a statistical distribution where, if the calculated test statistic falls, the null hypothesis is rejected. It is defined before testing, based on the chosen significance level, and represents extreme outcomes.

The basic steps are (1) state the null and alternative hypotheses, (2) set the significance level (α), (3) collect sample data, (4) calculate the test statistic, (5) find the p-value, (6) compare the p-value with α, and (7) make a decision to accept or reject the null hypothesis.

Data visualization converts raw data into meaningful visual forms, making large datasets easier to understand. It highlights trends, distributions, and variations, makes results easier to communicate to both technical and non-technical audiences, and reduces errors by making unusual patterns visible.

Bias in data collection occurs when data does not fairly represent all groups, often due to limited data sources or unfair sampling methods. This leads to inaccurate and misleading analysis results, for example a survey conducted only in top-performing schools.

Ethical use of data is important because it respects the privacy and confidentiality of individuals, ensures data is collected with consent and used only for intended purposes, and prevents discrimination by models. It builds trust among users and ensures a positive social impact.